Recycle old newspapers. If you are holding onto some paper for kindling, keep it near the location you’ll need it.
If you're holding onto newspapers recording historical events, consider that thousands were printed, and the item is unlikely to have a monetary value. Also, paper items rely heavily on condition, so even if it had value, if the newspapers were casually stacked in less than ideal conditions, that value is minimized.
And, if you are holding onto the papers for their historic value because your kids or grandkids will want them, consider if this is really the case. If they need to research these events, they’ll do so on the Internet, not by sorting through old newspapers.
If the papers have a personal value to you – perhaps you appeared in a flattering newspaper story – consider if you need a stack of newspapers or if you’d rather frame the article so you connect with this moment more easily.